Can A Filter Fix This?

I took this picture using a polarizer to try cutting through the haze a bit, without much success. As you can see by the darkened sky along the left, the sun was mostly behind me, and the polarizer was not in full effect. Would the polarizer have removed more of the haze if the sun had been at a different angle? Is a UV or haze filter better for high-altitude shots on days like this? Thank you for your help!